Hi, BOL, sorry, but Polycarp sounds like a fish, lol.
All believers make up the universal Church, and another word for universal is catholic. Perhaps the organization that came to be known as the Catholic Church should have chosen another name because it has NEVER represented ALL believers on earth at any one time. IF Polycarp was saying that it did, then he had it wrong. At present, the CC doesn't even represent most believers on earth.
I believe it was Jesus Christ who said, "For where two or three are gathered together in my name, there am I in the midst of them” (Matt 18:20).